Fourier method for inverse source problem using correlation of passive measurements*

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-09-04 DOI:10.1088/1361-6420/ad6fc7

Faouzi Triki, Kristoffer Linder-Steinlein, Mirza Karamehmedović

引用次数: 0

Abstract

We consider the inverse source problem for the time-dependent, constant-coefficient wave equation with Cauchy data and passive cross-correlation data.We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we show that the cross-correlation solves a wave equation, and we reconstruct the cross-correlation from boundary data to recover the source in the original Cauchy wave equation. In addition, we show the inverse source problem is ill-posed and suffers from non-uniqueness when the mean of the source is zero and provide a uniqueness result and stability estimate in case of non-zero mean sources.

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利用被动测量相关性解决逆源问题的傅立叶方法*

我们考虑了具有 Cauchy 数据和被动交叉相关数据的随时间变化的恒系数波方程的反源问题。我们建议将交叉相关视为波方程本身，并在源的支持下重建交叉相关，以获得原始 Cauchy 波方程。在获得源支持中的交叉相关性后，我们证明交叉相关性求解了一个波方程，并从边界数据中重建交叉相关性，以恢复原始考奇波方程中的源。此外，我们还证明了当源的均值为零时，逆源问题是求解困难且存在非唯一性的，并提供了非零均值源情况下的唯一性结果和稳定性估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.